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I've been reading this article https://en.wikipedia.org/wiki/Celestial_coordinate_system and a question came to my mind.
The minimum units are seconds ( ″ ). I picture an angle of 1 second as being like a "cone" going out from Earth. It's really small at the beginning but as you go further its width increases.
How wide does this cone get as you get further into the universe? How big is an arcsecond on different astronomical bodies?
How big is one arcsecond at various distances?
An arcsecond is a small angle, 1/3600 of a degree or about 5 millionths of a radian ($4.85\times10^{-6}$). To estimate the size of something that appears 1 arcsecond across you can use the small angle approximation to trigonometry: Multiply the distance to the object by $4.85\times10^{-6}$
Examples:
The atmosphere limits how much detail you can see. Typically the smallest detail you can see is about 3 or 4 arcseconds, though professional telescopes do better by being built on the top of mountains and using various tricks, like adaptive optics.
James K's answer is right on, and probably what you're after. I just wanted to mention an effect which comes into play if you look really, really far away:
Because light moves at a finite speed, we see galaxies (and other things) as they were in the past. And because the Universe expands, everything was closer together in the past, so we see distant galaxies as they were when they were closer and hence spanned a larger angle on the sky.
Thus, we have two competing effects: On the one hand, galaxies become smaller and smaller with distance, as expected and as decribed in James K's answer. On the other hand, we look further and further into the past, and hence see galaxies at a time when they looked larger and larger. The result — which is obtained by integrating the Friedmann equation — is that galaxies become smaller and smaller out to a certain distance (roughly 15 billion lightyears), after which the second effect starts to dominate and they start to grow in size.
Or, in other words, an arcseconds spans a larger and larger physical size (as described by James K) out to ~15 Gly (where it spans roughly 28,000 lightyears), after which it spans a smaller and smaller size. The relation looks like this:
You can do your own calculations easily, no need to ask anyone. Just change the distance units in the examples below:
